Statistics Formulas Used on Stat Trek

This web page lists statistics formulas used in the Stat Trek tutorials. Each formula links to a web page that explains how to use the formula.

Statistics

Unless otherwise noted, these formulas assume simple random sampling.

Random Variables

In the following formulas, X and Y are random variables, and a and b are constants.

Linear Transformations

For the following formulas, assume that Y is a linear transformation of the random variable X, defined by the equation: Y = aX + b.

Degrees of Freedom

The correct formula for degrees of freedom (DF) depends on the situation (the nature of the test statistic, the number of samples, underlying assumptions, etc.).

Sample Size

Below, the first two formulas find the smallest sample sizes required to achieve a fixed margin of error, using simple random sampling. The third formula assigns sample to strata, based on a proportionate design. The fourth formula, Neyman allocation, uses stratified sampling to minimize variance, given a fixed sample size. And the last formula, optimum allocation, uses stratified sampling to minimize variance, given a fixed budget.